In Chinese reporting it was quoted that Deng mentioned to Thatcher: "the PLA will march over across the Shenzhen river to HK on Jul 1, 1997 one way or another."
The official Chinese newspaper also famously showed a picture of Thatcher losing her footing coming out of the meeting hall.
It was an empty threat though; HK had a huge economy relative to China at the time (and more importantly a well-developed western-connected banking system). If push came to shove they might eventually do that but Deng was highly motivated to avoid such a conflict (imagine what that kind of political instability would have done to China's nascent economic reforms).
The fact that Britain even come to the negotiation table is a sign that their bottom line is much higher than military actions. Don't be silly to think a prime minister does not know the military power in her command...
The official Chinese newspaper also famously showed a picture of Thatcher losing her footing coming out of the meeting hall.
https://www.youtube.com/watch?v=fJdO-c8vuYc